A random permutation model appropriate to two-stage cluster sampling is presented and the optimal model-unbiased (prediction) estimator of a finite population mean is obtained. The prediction estimator is compared, in an empirical study with a variety of real populations, to the classical estimator used in PPS (probability proportional to size) sampling of the clusters. The study has shown that the prediction estimator may be only marginally better, in terms of efficiency, than the classical estimator in PPS sampling. The special cases of stratified sampling and uni-stage cluster sampling are also studied.